Stabalizing an egg drop project

1. The problem statement, all variables and given/known data
I have designed an egg drop project that performs just as I had hoped and portected the egg perfectly. I would need to make the object as stable as possible while it is falling.
My container is the foam molds that held the screen for my computer. The structure of the foam was designed to squish out. This allows the egg, which i have put in a larger cardboard egg filled with foam, to slide down slightly. The foams absorbs most of the impact and the friction on the cardboard egg the rest. My issue is i am graded on accuracy and weight. i cannot go over 300 grams i am currently at 201.5 grams. I must also hit a 30 cm by 30 cm for full points. Due to the shape of the foam it is hard to achieve a straight drop. I need a way to stabalize the egg without inhibiting it from free falling.2. Relevant equations
Momentum and force equations an impulse
F=ma
P=mv
J=Ft

3. The attempt at a solution
I was considering weighing the bottom end or using a streamer ontop, though i do not know how effective the streamer would be.1. The problem statement, all variables and given/known data